Propositiones ad Acuendos Juvenes/Problems/11 - De Duobus Hominibus Singulas Sorores Accipientibus/Variant 1

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Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $\text {11 a}$

De Duobus Hominibus Singulas Matres Accipientibus
Two men marrying each other's mother
If two men take the other's mother in marriage,
what is the relationship between their sons?


Solution

Each son is simultaneously the nephew and the uncle of the other.

Let the people involved be:

man $1$ and mother $1$
man $2$ and mother $2$
Let son $1$ be the son of man $1$ and mother $2$.
Let son $2$ be the son of man $2$ and mother $1$.

Then:

$(1): \quad$ Son $1$ and man $2$ are both the sons of mother $2$, which makes son $1$ the uncle of son $2$

and at the same time:

$(2): \quad$ Son $2$ and man $1$ are both the sons of mother $1$, which makes son $1$ the nephew of son $2$

and vice versa.


Historical Note

According to David Singmaster, this problem, along with two related problems (no pun intended) originating from Bede which he also documents, are the earliest of the strange family type.


There are contemporary examples of such:

At 52, Rolling Stones bassist Bill Wyman married 18-year-old Mandy Smith but divorced after a year.
Bill's 30-year-old son then, Stephen married Mandy's mother, age 46.
Therefore, Bill became the father-in-law of his ex mother-in-law
as well as the stepgrandfather of his former wife.


Sources

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